Method for producing a solid body including a microstructure

ABSTRACT

According to a method for producing a solid body ( 1 ) including a microstructure ( 2 ), the surface of a substrate ( 3 ) is provided with a masking layer ( 6 ) that is impermeable to a substance to be applied. The substance is then incorporated into the substrate regions not covered by the masking layer ( 6 ). A heat treatment is used to diffuse the substance into a substrate region covered by the masking layer ( 6 ) such that a concentration gradient of the substance is created in the substrate region covered by the masking layer ( 6 ), proceeding from the edge of the masking layer ( 6 ) inward with increasing distance from the edge. The masking layer ( 6 ) is then removed to expose the substrate region under this layer, and a near-surface layer of the substrate ( 3 ) in the exposed substrate region is converted by a chemical conversion reaction into a coating ( 9 ) which has a layer thickness profile corresponding to the concentration gradient of the substance contained in this near-surface layer. A supplementary treatment is implemented in a subsection of the coating ( 9 ) in which the thickness of the coating ( 9 ) is reduced.

BACKGROUND OF THE INVENTION

The invention relates to a method for producing a solid body including amicrostructure, especially, a semiconductor element, wherein the surfaceof a substrate is provided with a masking layer which is impermeable toa substance to be applied, and wherein the substance is subsequentlyincorporated into substrate regions not covered by the masking layer.

A process of this type is known from the book IntegrierteDigitalbausteine [Integrated Digital Components], Siemens AG (1970),pages 12 and 13. According to this process, to produce a semiconductorelement, a surface region of a silicon substrate is covered by a maskinglayer which consists of silicon dioxide and is impermeable to a dopant,while other surface regions remain exposed. To create the masking layer,the substrate is first placed in a stream of oxygen where a continuoussilicon dioxide layer is formed on the surface of the substrate. Alight-sensitive photoresist is then applied to the substrate surface.This photoresist is exposed through a photomask which transmits light atthose sites at which the substrate is to remain exposed for doping.After exposure, the photoresist is removed with a solvent from theexposed sites, while the unexposed regions of the photoresist which areinsoluble by the solvent remain on the substrate. An etching agent isthen used to etch away the silicon dioxide from the resist-free sites,after which the remaining photoresist is removed. The substrate is thenexposed at a temperature of approximately 1000° C. to a gas phasecontaining the dopant, during which the dopant diffuses into the opensubstrate sites not covered by the silicon dioxide. When the substratecools, the diffusion process ceases. The substrate has then been dopedregionally at the intended sites. The method may be used, for example,to integrate transistors, diodes, or electronic functional elements inthe substrate.

The previously known method has the disadvantage, however, that thecosts of the exposure device required to expose the substrate increasesignificantly as the size of the microstructures to be produceddecrease—see F&M, Volume 107 (1994), Number 4, pages 57–60, and Number9, pages 40–44. A principal disadvantageous aspect is that theresolution of the exposure device must be dimensioned for the smalleststructure to be produced on the substrate even when large structures aresimultaneously generated on the substrate. The production of solidbodies with the smallest structures is therefore complex and expensive.

European Patent 0 412 263 A2 describes a method for producing a via holein an integrated semiconductor circuit in which according to the method,a mask is used to dope a semiconductor body, and then oxidize thesurface of the semiconductor body, thereby creating an oxidation layerwhich is thicker in the doped semiconductor regions than in the undopedsemiconductor regions. An etching process is then used to remove thethinner section of the oxidation layer so as to be able to contact thesemiconductor body. IBM Technical Disclosure Bulletin, Volume 27, No.11, April 1985, pages 6533–6536 discloses an analogous method forproducing an insulation layer including regionally thinner sections on asemiconductor body, wherein the semiconductor body is doped throughthese thinner sections of the insulation layer.

Japanese Patent 02 077135 (Patent Abstracts of Japan) discloses a methodin which a gate oxide layer is applied to a silicon substrate.Polysilicon is deposited and structured on this gate oxide layer, a baselayer being produced as a mask using the structured polysilicon. Anitride layer is then deposited and structured, a source layer beingproduced as a mask using the nitride layer. A thick oxide layer issubsequently produced by selective oxidation and the nitride layer isremoved, so that a highly doped layer is produced as a mask using thethick oxide layer. An intermediate layer is then deposited, therebyproducing a via hole and an electrode.

U.S. Pat. No. 5,171,705 describes a method for producing a DMOStransistor in which a self-adjusting body connection contact isproduced.

There is a need for a method which provides inexpensive production of asolid body with a small structure.

SUMMARY OF THE INVENTION

An applied substance is diffused into a substrate layer covered by themasking layer in such a way that a concentration gradient of thesubstance is created, proceeding from the edge of the masking layerinward with increasing distance from the edge, in the substrate regioncovered by the masking layer. The masking layer is next removed toexpose the substrate region below it. A layer of the substrate near thesurface in the exposed substrate region is converted by a chemicalconversion reaction into a coating with a layer thickness profilecorresponding to the concentration gradient of the substance containedin this near-surface layer; and wherein a supplementary treatment isimplemented in a subsection of the coating, the surface of which issmaller than the substrate surface covered by the original masking layerand in which the thickness of the coating is reduced relative to theremaining subsections of the coating, in which treatment the substrateregion covered by this subsection is exposed, and/or a material isincorporated into this substrate region through the coating.

As a result of this heat treatment, the region of the substrateincluding the incorporated substance is thus enlarged, the substancebeing subdiffused underneath the edge of the masking layer. Aconcentration gradient with a locus-dependent concentration of thesubstance is created in the substrate region covered by the maskinglayer, with the concentration decreasing in the substrate plane runningalong the interface of the masking layer and substrate, and proceedingfrom the edge of the masking layer inward with increasing distance fromthe edge. The coating which was created, after removal of the maskinglayer, by the chemical conversion reaction of the substrate regionoriginally covered by the masking layer has a thickness at differentsites of the substrate layer which corresponds to the concentration ofthe substance at the respective site. Depending on the chemicalconversion reaction selected, the layer thickness of the coating alongthe substrate plane may either decrease or increase, proceeding from theedge of the substrate layer originally covered by the masking layertoward the interior of this substrate layer. Appropriate chemicalconversion reactions are already well known. The supplementary treatmentdependent on the layer thickness may be advantageously implemented forthe substrate in a given region which is smaller than the regionoriginally covered by the masking layer. During the supplementarytreatment of the coating for example, the entire surface of the coatingfacing away from the substrate may be removed until a subsection of thesubstrate region originally covered by the coating is exposed at thesites in which the original thickness of the coating was smaller than atthe remaining sites of the coating. In addition, however, thesupplementary treatment may also incorporate a chemical substance into asubsection of the substrate region covered by the coating through thecoating, for example by diffusion or bombardment with particles. In thisprocess, the layer thickness profile of the coating is matched to thediffusion properties of the substance and/or to the kinetic energy ofthe particles in such a way that the substance is able to penetrate thecoating only regionally at those sites where the layer thickness doesnot exceed a specified thickness.

In a masking layer which was created on the substrate by aphotolithographic process, a structure may be produced, the dimensionsof which are smaller than the dimensions of the smallest substratesurface still to be masked off from the light or still to be exposed,due to the limited resolution of the exposure device used for thephotolithographic process. As a result, a cost-effective exposure devicemay be advantageously employed which has a lower resolution than thatrequired for the dimensions of the smallest structure to be produced.The method is especially well suited for producing solid bodies thathave both small and large structures.

In an advantageous embodiment of the invention, the substrate regionslaterally adjoining the masking layer are covered with an etching maskand the masking layer is then contacted with an etching agent. Theetching mask is preferably created by a chemical reaction in which anear-surface layer of the substrate regions to be covered by the etchingmask is converted into an etching mask material. The etching mask may beapplied to the surface regions not covered by the masking layer in asimple manner and without the use of a supplementary photolithographicstep. To accomplish this, the near-surface layer may, for example, beconverted in a nitrogen atmosphere to a nitride layer resistant to thespecific etching agent. The entire surface of the solid body may then becontacted with the etching agent to remove the masking layer. In theevent the etching mask is of a greater thickness than the masking layer,another etching agent may be employed which removes the etching mask inaddition to the masking layer from the solid body. In this case, theetching rates and the thicknesses of the masking layer and etching maskmust be matched to each other in such a way that, after the completeremoval of the masking layer by the etching agent, the etching maskstill possesses a residual thickness so as to continue to cover thesubstrate.

It is especially advantageous if the etching mask is created during theheat treatment in an oxygen-containing atmosphere while the substratematerial is undergoing oxidation. This allows an additional fabricationstep to be eliminated in the production of the etching mask.

It is advantageous if the chemical conversion reaction is an oxidationreaction. The coating may then be generated easily in anoxygen-containing atmosphere and, if required, with the input of energy.In the process, especially in the case of a silicon substrate into whicha dopant has been diffused, a clear shaping of the layer profile of thecoating is obtained as a function of the concentration gradient of thedopant in the substrate material.

In an advantageous embodiment of the invention, the near-surface layerof the substrate is converted by a chemical conversion reaction into anelectrically insulating coating in the substrate region in which themasking layer has been removed. After the regional removal of thecoating, a metal coating is electrolytically deposited on the exposedsurface of the electrically conductive substrate region. As a result, itis possible, for example, to apply a microelectrode and/or a conductivetrack of small dimensions onto the substrate. The electrodeposition ofthe metal coating may be implemented specifically by a currentlesstechnique.

It is advantageous for a preferably metallic surface layer to be appliedto the surface of the solid body, and for the adhesive properties of thesubstrate material and of the coating to be matched to the material ofthe surface layer such that this layer continues to adhere only to theexposed subsection of the substrate region. The material of the surfacelayer here is selected so as to adhere more effectively to the exposedsubsection of the surface region than to adjacent surface regions of thecoating. Any layer regions adhering to the adjacent surface regionsafter coating may then, for example, be mechanically etched from thesurface of the solid body, while the region of the surface layeradhering to the exposed subsection of the substrate region continues toadhere to this region. If required, the surface layer may also bemechanically stressed by the incorporation of impurities. When the layerregions adhering to the coating are detached, cracks may form along theperiphery of the surface of the exposed subsection of the substrateregion, the cracks facilitating the removal of the regions of thissurface layer adhering to the coating.

In one embodiment of the invention, the near-surface layer of thesubstrate is converted by a chemical conversion reaction to a coatingwhich is impermeable to the chemical substance to be applied. During thesupplementary treatment, the substrate region covered by a subsection ofthis coating is first exposed, then the substance is incorporated intothis substrate region. Incorporation of the substance, which may inparticular be a dopant for the semiconductor substrate, may, forexample, be implemented by diffusion or bombardment with particles—withthe substance penetrating the exposed substrate region, while in thoseregions of the substrate covered by the coating, any penetration of thesubstance into the substrate is prevented by the coating.

In one embodiment of the invention, a heat treatment is used to diffusethe incorporated substance into a substrate region covered by themasking layer such that, proceeding from the edge of the masking layerinward with increasing distance from the edge of the masking layer, aconcentration gradient of the substance is created in the substrateregion covered by the masking layer. The masking layer is subsequentlyremoved to expose the substrate region below it. A layer of thesubstrate near the surface in the exposed substrate region is convertedby a chemical conversion reaction into a coating with an appropriatelayer thickness profile corresponding to the concentration gradient ofthe substance contained in this near-surface layer. A supplementarytreatment is implemented in a subsection of the coating, the surface ofwhich is smaller than the substrate surface covered by the originalmasking layer and in which the thickness of the coating is reducedrelative to the remaining subsections of the coating, in which treatmentthe substrate region covered by this subsection is exposed, and/or achemical substance is incorporated into this substrate region throughthe coating. The medium, the material of the coating laterally adjacentto the exposed substrate region, and/or the reaction conditions arepreferably selected such that no chemical reaction occurs between themedium and the material of the coating. The chemical reaction is thenlimited to the exposed subsection of the substrate region such that thissection may be chemically modified in a targeted fashion.

In one embodiment of the invention, after exposure of the substrateregion, the substrate region is contacted with an etching agent for thesubstrate material, to which the coating surrounding the substrateregion is essentially chemically resistant, in order to insert adepression in the substrate region. The coating then forms an etchingmask for the etching agent. An anisotropic etching agent may be used toinsert a groove with a roughly V-shaped cross-section into the substrateregion. The solid body may be a component of a microreactor, the etcheddepression forming, for example, a supply channel for a substance to beinserted into the chamber of the microreactor, and/or forming adischarge channel for a substance to be discharged from the chamber. Ametallic material is preferably used as the substrate for one componentof the microreactor, for example aluminum or silver, which materialprovides effective dissipation of heat from or into the chamber of themicroreactor.

These and other objects, features and advantages of the presentinvention will become more apparent in light of the following detaileddescription of preferred embodiments thereof, as illustrated in theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-section through a solid body provided to produce asemiconductor element, into the substrate of which doping regions areincorporated laterally on both sides of the masking layer;

FIG. 2 shows the solid body seen in FIG. 1 after a heat treatment inwhich the doping material is diffused underneath the masking layer;

FIG. 3 shows the solid body seen in FIG. 2 after removal of the maskinglayer and subsequent application of a coating including a thicknessprofile;

FIG. 4 shows the solid body seen in FIG. 3 after the etching process inwhich the coating has been removed regionally from the substrate;

FIG. 5 shows the solid body seen in FIG. 4 after the selectiveapplication of a metal coating; and

FIG. 6 is a cross-section through a DMOS transistor cell.

DETAILED DESCRIPTION OF THE INVENTION

In a method for producing a solid body 1 with a microstructure in theform of a semiconductor element, a substrate 3 that includes preferablysilicon is provided, which substrate has passivation layers 4 thatinclude silicon dioxide on its surface, the layers covering thesubstrate 3 continuously. Using a known method such as photolithographicapplication of an etch-resistant mask and followed by a wet etchingprocess, an opening 5 is incorporated into the passivation layer 4, theopening exposing a subsection of the substrate 3. To produce a maskinglayer 6, a silicon nitride layer is applied through the opening 5 by acoating method such as chemical vapor deposition, over the entiresubstrate region exposed in the opening 5. Subsequently, an etching maskresistant to an etching agent such as phosphoric acid is applied to thislayer by a photolithographic procedure, which mask covers certainregions of the silicon nitride layer. The solid body 1 is then contactedwith the etching agent to remove those regions of the silicon dioxidelayer not covered by the etching mask. The etching mask is then removed.It is evident in FIG. 2 that the regions of the silicon nitride layerremaining on the substrate 3 form the masking layer 6 which covers asubsection of the substrate region located in the opening 5, and thatthis masking layer 6 is spaced laterally on both sides of thepassivation layer 4. The material of the masking layer 6 is selectedbased on its impermeability to a substance provided for doping thesubstrate, for example boron or phosphorus.

After the masking layer 6 is produced, this substance is inserted intothe opening 5 to dope the substrate regions not covered by the maskinglayer 6. This may be accomplished for example by exposing the solid body1 to a gas stream containing the substance. The substance then diffusesinto the substrate regions not covered by the masking layer 6 where itforms doping zones 7 (FIG. 1).

After and/or during the incorporation of the substance into the dopingregions 7, a heat treatment is implemented in which the incorporatedsubstance is diffused into a substrate region covered by the maskinglayer 6. The heat treatment may be performed at a temperature of, forexample, 1000° C. It is clearly evident in FIG. 2 that the dopingregions 7 have expanded relative to FIG. 1 and that the dopant hassub-diffused underneath the edge of the masking layer 6. Upon completionof the heat treatment, there is a decrease in the concentration of thesubstance in the coverage plane of the doping regions 7, proceeding fromthe masking layer 6 into the substrate region covered by the maskinglayer 6 and with increasing distance from the edge of the masking layer.

During the heat treatment, the solid body 1 is exposed to anoxygen-containing atmosphere in which an oxide layer is deposited in theopening onto the substrate region not covered by the masking layer 6,the oxide layer forming an etching mask 8 which is resistant to anetching agent, such as phosphoric acid, used to remove the masking layer6. After completion of the heat treatment, the masking layer 6 iscontacted with this etching agent to remove the masking layer 6, thusexposing the substrate region located under the masking layer 6.

Next, a layer of substrate 3 located under the exposed substrate regionis converted by a chemical conversion reaction in an oxygen-containingatmosphere into a silicon dioxide coating 9. The local thickness of thiscoating 9 is dependent on the concentration of the substance diffusedinto the specific substrate region taking part in the chemicalconversion reaction. It is clearly evident in FIG. 3, that the thicknessof the coating 9 decreases proceeding from the edge of the coating 9toward the center of the coating 9, specifically, in accordance with therespective decrease in concentration of the substance in the substrate3.

In the embodiment of FIG. 4, the coating 9 is exposed to an etchingagent which etches away the material from the surface of the coating 9facing away from the substrate 3. The etching process is stopped when asubsection of the coating 9, in which the original thickness of thecoating 9 relative to the adjacent subsections of the original coating 9is reduced, is completely removed, and the substrate 3 covered by thissubsection is exposed. It is evident from FIG. 4 that after completionof the etching process, the substrate region covered by the originalmasking layer 6 remains covered by the coating 9 only along itsperipheral regions, and that a substrate region which is smaller thanthe substrate region covered by the original masking layer 6 has beenexposed. While near-surface layers are also removed during the etchingof the coating 9 from the passivation layer 4 and the etching mask 8,the thickness of the passivation layer 4 and that of the etching mask 8are adjusted to be large enough so only part of their thickness isetched away, and, as a result, the substrate material located beneaththem continues to remain covered after completion of the etchingprocess.

In the embodiment of FIG. 5, the coating 9 includes an electricallyinsulating material. After regional removal of the coating 9, a metallayer 10 is electrolytically deposited on the exposed surface of thesubstrate 3, which layer may form, for example, an electrode or aconductive track. It is clearly evident from FIG. 5 that the dimensions“b” of the metal layer 10 are smaller than the dimensions “a” of theoriginal masking layer 6. The method may thus be employed to produce amicrostructure 2, the dimensions of which are smaller than theresolution of an exposure device used during the photolithographprocessing applied to the masking layer 6. As a result, the additionalcosts otherwise required for a high-resolution exposure device may beeliminated.

A substance may be incorporated into the substrate region exposed by theregional removal of the coating 9. The material of the coating 9 isselected based on the fact that the residual amount of the coating 9remaining on the substrate 3 after exposure of the substrate region isimpermeable, at least regionally, to the substance to be incorporated.In order to incorporate the substance, the solid body is contacted witha substance, for example in a gas phase, that essentially diffuses onlyinto the exposed substrate regions while the remaining substrate regionsremain free of the substance.

FIG. 6 shows a DMOS transistor device produced according to the method,in which device the substance is a dopant which is incorporated into ap⁺ zone 15 for a freewheeling diode. The doping regions 7 located onboth sides of the p⁺ zone 15 are n⁺ source regions which are embedded ina p-doped substrate region 11. This p-doped substrate region 11 is inturn embedded in an n-doped substrate region 12. Also visible in FIG. 6are gate contacts 13, a passivation layer 4, a source contact 14, and agate oxide layer 16.

In the method to produce the solid body 1 with the microstructure 2, thesurface of the substrate 3 is thus provided with the masking layer 6which is impermeable to the substance to be applied. The substance isthen incorporated into substrate regions not covered by the maskinglayer 6. A heat treatment is used to diffuse the substance into aspecific substrate region covered by the masking layer 6 such that aconcentration gradient of the substance is created, proceeding from theedge of the masking layer inward with increasing distance from the edge.The masking layer 6 is subsequently removed to expose the substrateregion below it, and a near-surface layer of the substrate 3 located inthe exposed substrate region is converted by a chemical conversionreaction into the coating 9 which has a layer thickness profilecorresponding to the concentration gradient of the substance containedin the near-surface layer. A supplementary treatment is implemented in asubsection of the coating 9 in which the thickness of the coating 9 hasbeen reduced.

Although the present invention has been illustrated and described withrespect to several preferred embodiments thereof, various changes,omissions and additions to the form and detail thereof, may be madetherein, without departing from the spirit and scope of the invention.

1. Method for producing a solid body including a microstructure, wherein the surface of a substrate is provided with a masking layer which is impermeable to a substance to be applied, and the substance is subsequently incorporated into substrate regions not covered by the masking layer, the method comprising the steps of: heat treating a substrate region covered by the masking layer to diffuse the incorporated substance in the substrate region covered by the masking layer, such that a concentration gradient of the substance is created, proceeding from the edge of the masking layer inward with increasing distance from the edge, in the substrate region covered by the masking layer; removing the masking layer to expose the substrate region below it; converting a layer of the substrate near the surface in the exposed substrate region by a chemical conversion reaction into a coating with a layer thickness profile corresponding to the concentration gradient of the substance contained in this near-surface layer; treating a subsection of the coating, the surface of which is smaller than the substrate surface covered by the original masking layer, and in which the thickness of the coating is reduced relative to the remaining subsections of the coating, in which treatment the substrate region covered by this subsection is exposed to provide an exposed subsection, and/or a material is incorporated into this substrate region through the coating, where during the removal of the masking layer, the substrate regions laterally adjacent to the masking layer are covered by an etching mask, and the masking layer is then contacted with an etching agent, and where a metallic layer is applied over the exposed subsection, and that the adhesive properties of the substrate material and of the coating are matched to the material of the surface layer such that the metallic layer adheres only to the exposed subsection of the substrate region.
 2. The method of claim 1, where the etching mask is created by a chemical reaction in which a near-surface layer of the substrate regions to be covered by the etching mask is converted to an etching mask material.
 3. The method of claim 2, where the etching mask is created during the heat treatment by thermal oxidation of the substrate material in an oxygen-containing atmosphere.
 4. The method of claim 3, where the chemical conversion reaction is an oxidation reaction.
 5. The method of claim 4, where the substrate region in which the masking layer has been removed, the near-surface layer of the substrate is converted by a chemical conversion reaction into an electrically insulating coating; and that, after the regional removal of the coating, the metal coating is electrolytically deposited on the exposed surface of the electrically conductive substrate region.
 6. The method of claim 5, where the near-surface layer of the substrate is converted by a chemical conversion reaction to a coating which is impermeable to a chemical layer to be applied.
 7. The method of claim 6, where the solid body is contacted by a medium, and that substrate material present in the exposed substrate region is converted by a chemical reaction with this medium into another material.
 8. The method of claim 7, where after exposing the substrate region, the substrate region is contacted with an etching agent for the substrate material, to which the coating surrounding the substrate region is essentially chemically resistant, in order to insert a depression into the substrate region.
 9. A method for producing a solid body including a semiconductor element, comprising: depositing a passivation layer on a surface of a semiconductor substrate; forming an opening in the passivation layer such that a section of the substrate surface is exposed; forming a silicon nitride layer on the section and etching portions of the silicon nitride layer to form a masking layer on a subsection of the section of the substrate surface, where the subsection is spaced laterally within the opening from sidewalls of the passivation layer; doping the substrate with a substance to form doping zones within the substrate, where the masking layer is impermeable to the substance; heat treating the semiconductor substrate to diffuse the substance within the doping zones into a substrate region that underlies the masking layer and is between the doping zones; forming oxide layers over regions of the substrate between the sidewalls of the passivation layer and not covered by the masking layer; removing the masking layer to provide an exposed substrate region; forming a silicon dioxide coating over the exposed substrate region, where the thickness of the silicon dioxide coating decreases towards the center of the exposed substrate region; applying an etching agent to remove the silicon dioxide coating in a center region of the exposed substrate region, where the center region is smaller than the area covered by the masking layer; and electrodepositing a metal layer over the center region.
 10. The method of claim 9, where the step of electrodepositing comprises a currentless technique.
 11. The method of claim 9, where the substance comprises boron.
 12. The method of claim 9, where the substance comprises phosphorus.
 13. The method of claim 9, where upon completion of said step of heating there is a decrease in the concentration of the substance in the coverage plane of the doping regions, proceeding from the masking layer into the substrate region covered by the masking layer and with increasing distance from the edge of the masking layer.
 14. A method for producing a solid body including a semiconductor element, comprising: depositing a passivation layer on a surface of a semiconductor substrate; forming an opening in the passivation layer such that a section of the substrate surface is exposed; forming a silicon nitride layer on the section and removing portions of the silicon nitride layer to form a masking layer on a subsection of the section of the substrate surface, where the subsection is spaced laterally within the opening from sidewalls of the passivation layer; doping the substrate with a dopant to form doping zones within the substrate, where the masking layer is impermeable to the dopant; heat treating the semiconductor substrate in an oxygen environment to diffuse the substance within the doping zones into a substrate region that underlies the masking layer and is between the doping zones, and form oxide layers over regions of the substrate between the sidewalls of the passivation layer and not covered by the masking layer; removing the masking layer to provide an exposed substrate region; forming a silicon dioxide coating over the exposed substrate region, where the thickness of the silicon dioxide coating decreases towards the center of the exposed substrate region; removing the silicon dioxide coating in a center region of the exposed substrate region, where the center region is smaller than the area covered by the masking layer; and electrolytically depositing a metal layer over the center region. 